Data reduction using a regressive discrete Fourier-transform technique

Abstract

With the development of optical measurement techniques it was possible to obtain vast amounts of data. In vibrometry applications in particular where FRF-matrices with tens of thousands of rows and an equal number of rows are stored, data reduction has become a point of interest. It has long been known that it is possible to reduce (approximate) the measurement data (e.g. mode shapes) by means of a Fourier decomposition. One of the most common techniques for evaluating optical measurement data is by means of a Fourier analysis. It is well known that for periodic and band-limited sequences the Discrete Fourier Transform (DFT) returns the true Fourier coefficients when exactly 1 period (or a multiple) is processed. Leakage will occur when less than 1 period is considered. This gives rise to non-negligible errors, which can be resolved by using a Regressive Discrete Fourier Transform (RDFT), introduced in this article. The measured signal is represented by a model using sines and cosines. The coefficients of those sines and cosines are then estimated on a global scale by means of a frequency domain system identification technique. By making use of the regressive technique proposed in this paper, it is possible to reduce the data in comparison to the classical Fourier decomposition even further by a sizeable factor. In this article the introduced method will be applied in particular to the reduction of data for (1D) laser vibrometer measurements performed on a composite (IPC) beam, as well as on an aluminum plate (2D). The proposed technique will also be validated on both 1D and 2D simulations of varying complexity.